Question

The length breadth and height of a cuboid are in the ratio 6:5:4. If its volume is 15000cm3 find its dimensions and its surface area?


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Answer 1

Answer:

length = 6x = 6*125 = 750

breadth = 5x = 5*125 = 625

height = 4x = 4*125 = 500

Step-by-step explanation:

let the length= 6x

breadth= 5x

height= 4x

So, volume of cuboid = l*b*h

a/q,

15000cm^3= 6x*5x*4x

15000 = 120x

x = 15000/120

x = 125

So,

length = 6x = 6*125 = 750

breadth = 5x = 5*125 = 625

height = 4x = 4*125 = 500

Now,we have to find surface area of cuboid

Surface area =2(lb+bh+hl)

=2(30×25+25×20+20×30)

=2(750+500+600)

 =3700cm²

Hope it helps you.

Answer 2

Given

length , breadth and height of cube are in the ratio 6:5:4

Volume of cuboid is 15000cm³

To Find

Dimensions of cuboid and its surface area

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

$\sf Volume \:of\: cube =length ×breadth×height$

$\sf Surface \:area\: of \:cube =2(lb+bh+hl)$

Step by step explanation

1. First step is to write down the formula of volume and place the values given in the Question and compare both sides.

sides are given in the ratio 6:5:4

assuming that it be 6x,5x &4x

Volume of cuboid =6x × 5x × 4x

=>15000=120x³

=>x³=15000/120

=>x³=1500/12

=>x³=125

x=5

length of cuboid =6x = 6×5=30 cm

Breadth of cuboid =5x=5×5=25cm

Height of cuboid=4x=4×5=20cm

Now,we have to find surface area of cuboid

Surface area =2(lb+bh+hl)

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:$=2(30×25+25×20+20×30)

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:$=2(750+500+600)

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:$=2(1850)

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:$=3700cm²